Capacitance
Capacitor A capacitor is a device that stores electric charge.
Capacitor applications: Computer RAM memory and keyboards.
Capacitor applications: Electronic flashes for cameras.
Capacitor applications: Electric power surge protectors.
Capacitor applications: Radios and electronic circuits.
Capacitor applications: ElectricPowerSupplies
TimingCircuits
VoltageStorageDeviceForCarStereos
Capacitors A basic capacitor has two parallel plates separated by an insulating material A basic capacitor has two parallel plates separated by an insulating material A capacitor stores an electrical charge between the two plates A capacitor stores an electrical charge between the two plates The unit of capacitance is Farads (F) The unit of capacitance is Farads (F) Capacitance values are normally smaller, such as µF, nF or pF Capacitance values are normally smaller, such as µF, nF or pF
Capacitors Basic capacitor construction Basic capacitor construction Dielectric material Plate 1 Plate 2 The dielectric material is an insulator therefore no current flows through the capacitor
Capacitors Storing a charge between the plates Electrons on the left plate are attracted toward the positive terminal of the voltage source Electrons on the left plate are attracted toward the positive terminal of the voltage source This leaves an excess of positively charged holes This leaves an excess of positively charged holes The electrons are pushed toward the right plate The electrons are pushed toward the right plate Excess electrons leave a negative charge Excess electrons leave a negative charge _ + _
Capacitors Types of capacitors The dielectric material determines the type of capacitor The dielectric material determines the type of capacitor Common types of capacitors are: Common types of capacitors are: Mica Mica Ceramic Ceramic Plastic film Plastic film
Capacitors Some capacitors are polarised, they can only be connected one way around Some capacitors are polarised, they can only be connected one way around Electrolytic capacitors are polarised Electrolytic capacitors are polarised
Capacitors Variable capacitors are used in communication equipment, radios, televisions and VCRs Variable capacitors are used in communication equipment, radios, televisions and VCRs They can be adjusted by consumers by tuning controls They can be adjusted by consumers by tuning controls Trimmers are internal adjusted capacitors that a consumer cannot adjust Trimmers are internal adjusted capacitors that a consumer cannot adjust
Capacitors These variable capacitors would be difficult to squeeze into your mobile phone and iPod These variable capacitors would be difficult to squeeze into your mobile phone and iPod Current technology uses semi-conductor variable capacitors called varactors (varicaps) Current technology uses semi-conductor variable capacitors called varactors (varicaps)
A capacitor consists of two conductors separated by an insulator, which could be air or even a vacuum. Capacitor Metal Plates Insulating Material (Dielectric)
Some Capacitors insulator conductor
Capacitance : Definition Take two chunks of conductor Take two chunks of conductor Separated by insulator Separated by insulator Apply a potential V between them Apply a potential V between them Charge (Q) will appear on the conductors, Charge (Q) will appear on the conductors, Q + = +CV Q + = +CV Q - = -CV Q - = -CV C depends upon both: C depends upon both: “geometry” “geometry” Insulator material (dielectric) Insulator material (dielectric) 0 V Q+ = +CV Q- = -CV V
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Types of Capacitors Parallel-Plate CapacitorCylindrical Capacitor A cylindrical capacitor is a parallel-plate capacitor that has been rolled up with an insulating layer between the plates.
Dielectrics - Insulator Air - Often used in radio tuning circuits
Dielectrics Ceramic - Used for high frequency purposes like antennas, X-ray and MRI machines antennasX-rayMRIantennasX-rayMRI
Dielectrics Mylar - Most commonly used for timer circuits like clocks, alarms and counters clocks
Dielectrics Glass - Good for high voltage applications Glass - Good for high voltage applications Glass
Dielectrics Super capacitor - Powers electric and hybrid cars electrichybrid carselectrichybrid cars
Calculating Capacitance? C = fn(geometry, dielectric) C = fn(geometry, dielectric) e.g. C = Area/separation = A/d for a parallel-plate capacitor e.g. C = Area/separation = A/d for a parallel-plate capacitor With much symmetry, C can be calculated With much symmetry, C can be calculated And capacitors are often manufactured in simple geometries! And capacitors are often manufactured in simple geometries! Without such symmetry – approximation and estimation is necessary Without such symmetry – approximation and estimation is necessary Can be made arbitrarily accurate Can be made arbitrarily accurate Remember Laplace and field plotting? Remember Laplace and field plotting? Tackle calculation, then estimation Tackle calculation, then estimation
Example 1 : Parallel-Plate Capacitor 1. Calculate field strength E as a function of charge ±Q on the plates 2. Integrate field to calculate potential V between the plates 3. Q=CV, C = V/Q Area A -Q E Dielectric constant Separation d Area A +Q V
Example 1 : Parallel-Plate Capacitor Gauss’s Law – D, E 0 only on bottom face Gauss’s Law – D, E 0 only on bottom face Charge enclosed = A G Q/A Charge enclosed = A G Q/A -Q/A Coulombs/m 2 E +Q/A Coulombs/m 2 Area A G
Example 1 : Parallel-Plate Capacitor Area A-Q dl E d Area A +Q âzâzâzâz
Example 1 : Parallel-Plate Capacitor Area A-Q dl E d Area A +Q âzâzâzâz
Example 2 : Cylindrical Capacitor Two concentric cylindrical conductors, overlap length L Two concentric cylindrical conductors, overlap length L e.g. co-axial TV lead cable e.g. co-axial TV lead cable Separated by a dielectric (insulator) Separated by a dielectric (insulator) 0 -Q V +Q E E 0 -Q V +Q L
Example 2 : Cylindrical Capacitor E 0V, -Q V +Q r a b CHECK NOTES
Estimating Capacitance … When the electrodes are not as symmetrical as these examples When the electrodes are not as symmetrical as these examples Also – our “ideal” parallel-plate capacitor should really look thus:- Also – our “ideal” parallel-plate capacitor should really look thus:- Fringing fields
Estimating Capacitance : Principle Sketch equipotentials and field lines using field plotting Sketch equipotentials and field lines using field plotting Can be arbitrarily accurate Can be arbitrarily accurate More accuracy means more V 0 = (V 1 +V 2 +V 3 +V 4 ) More accuracy means more V 0 = ¼ (V 1 +V 2 +V 3 +V 4 ) Use a computer! Use a computer!
Underlying Idea … C = A/d = 5x2x/2x C = 5 x Is 100% equivalent to 5x 2x x x x Each C = A/d = x 10 in parallel, 2 in series C TOT = 10 x /2 = 5 x
Underlying Idea … These plates are all the same potential = an equipotential
Negative electrode Equipotential Estimation : Example Positive electrode
Estimation : Example x x x
Estimating Capacitance : Recipe Draw equipotentials as accurately as you have time for Draw equipotentials as accurately as you have time for Using field mapping in reality Using field mapping in reality Draw field lines to make square “cells” (cubes in 3D) Draw field lines to make square “cells” (cubes in 3D) Field line and equipotentials cross at 90° Field line and equipotentials cross at 90° Make cells as square as possible Make cells as square as possible Count series and parallel – each is a capacitance of x ( per unit depth when using a 2D diagram) Count series and parallel – each is a capacitance of x ( per unit depth when using a 2D diagram)
Estimation : Example Each of these is A/d = xx/x 4 in series, 30 in parallel Capacitance = 30x/4 Or capacitance/unit depth = 10/4 depth 4x 10x 3x x x x
RC Time Constant T = RC
The time it takes for a capacitor to charge to 63.2% or discharge to 36.8% of the maximum voltage. RC Time Constant
Capacitance in AC Circuits
Capacitive Reactance
Find the current flowing in a circuit when a 4uF capacitor is connected across a 880v, 60Hz supply.